CND-16

Sommerfeld Seebeck

S = − (π² k_B² T) / (3 e E_F) for a free-electron metal. Thermopower.

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Electrons in solidsSeebeck

Governing equation

S=-\dfrac{\pi^2 k_B^2 T}{3 e E_F}

$T \in \left[20, 800\right]$

where

T: Temperature (K)
E_F: Fermi energy (eV)
S: Seebeck (µV/K)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

S=-\dfrac{\pi^2 k_B^2 T}{3 e E_F}

$T \in \left[20, 800\right]$

$T = 20$ $S = -0.07$

Along the curve

②

Domain of the variable — blue

T_{\min} = 20,\quad T_{\max} = 800

$T \in \left[20, 800\right]$

$T = 20$ $T = 20$

Along the curve

③

Response curve — green

S=-\dfrac{\pi^2 k_B^2 T}{3 e E_F}

$T \in \left[20, 800\right]$

$T = 20$ $S = -0.07$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}S}{\mathrm{d}T}

$T \in \left[20, 800\right]$

$T = 24.91$ $S^{\prime} = -0.003$

Along the curve

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-16 — Sommerfeld Seebeck) is the form associated with Seebeck. Working symbols: $T$ , $E_F$ $\rightarrow$ $S$ . Metals have |S| of a few µV/K. Semiconductors are much larger and signed by the carrier.

Purpose

Purpose: compute

S

from

T

E_F

in Condensed matter via

S=-\dfrac{\pi^2 k_B^2 T}{3 e E_F}

S = − (π² k_B² T) / (3 e E_F) for a free-electron metal. Thermopower. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

T = 300.000\,\mathrm{K}

E_F = 7.000\,\mathrm{eV}

, the governing relation

S=-\dfrac{\pi^2 k_B^2 T}{3 e E_F}

yields

S = -1.05\,\mathrm{\mu V/K}

. A bar with two temperatures, a voltage. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Temperature T300 KFermi energy E_F7 eV

Outputs

Seebeck S-1.05 µV/K

Reading speed

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Narration of this film

A bar with two temperatures, a voltage.

Metals have |S| of a few µV/K. Semiconductors are much larger and signed by the carrier.

Reading speed

Watch on YouTube